Answer:
5/6
Step-by-step explanation:
The complement of rolling 6 will be all the possible outcomes except rolling 6 which is 5/6
A(1) = 6 = d + c
<span>a(4) = 33 = 4d + c </span>
<span>3d = 27=> d=9 </span>
<span>c = -3 </span>
<span>a(2) = 9(2) - 3 = 15 </span>
<span>a(3) = 15 + 9 = 24</span>
A.) Let the length of the sides of the bottom of the box be y and z, and let the length of the sides of the square cut-outs be x, then
V = xyz . . . (1)
2x + y = 24 => y = 24 - 2x . . . (2)
2x + z = 24 => z = 24 - 2x . . . (3)
Putting (2) and (3) into (1), gives:
V = x(24 - 2x)(24 - 2x) = x(24 - 2x)^2 = x(576 - 96x + 4x^2)
V = 4x^3 - 96x^2 + 576x
b.) For maximum volume, dV/dx = 0
dV/dx = 12x^2 - 192x + 576 = 0
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x = 4 or x = 12
but x = 12 is unrearistice
Therefore, x = 4.
y = z = 24 - 2(4) = 24 - 8 = 16
Therefore, the dimensions of the box that enclose the largest possible volume is 16 inches by 16 inches by 4 inches.
c.) Maximum volume = 16 x 16 x 4 = 1024 cubic inches.
In order to figure this out, we need to find the price per ounce of candy. We can do this by dividing the price of the candy by the amount of ounces of candy that were bought.
Tiffany bought 3 ounces and paid 46 cents, so she bought candy with a rate of 46/3 = 15.33 cents per ounce.
Tony bought 13 ounces of candy and paid 76 cents. He bought candy with a rate of 76/13 = 5.85 cents per ounce.
Because Tony is paying less for each ounce, he made the better buy.
2. a) absolute values for the slopes
y = mx + c
3/4, 9,-11, -1 = 3/4, 9,11, 1
the higher the slope, the steeper the graph. 11 is high,
y = -11x - 5
b) 1/4,3,-3/4,-8 = 1/4,3,3/4,8
smaller value is 3/4
the least steep graph will be in,
y = -3/4x + 7
c) 6,2,1, 1/2
1/2 is the smallest value.
y = 1/2x + 6
d) It would be less steep.
e) It would be shifted down.
f) y = -8x - 3
g) y = 1/4x + 9
h) y = 3x - 1
i) y = -5x - 10
